MinT - Information on Result #1205227

Information on Result #1205227

Digital (118, 126, large)-net over F₄, using trace code for nets based on digital (34, 42, 4194300)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64⁴², 4194300, F₆₄, 10, 8) (dual of [(4194300, 10), 41942958, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁴², 8388601, F₆₄, 2, 8) (dual of [(8388601, 2), 16777160, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴², 8388602, F₆₄, 2, 8) (dual of [(8388602, 2), 16777162, 9]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(64¹³, 4194301, F₆₄, 2, 4) (dual of [(4194301, 2), 8388589, 5]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64¹³, 8388602, F₆₄, 4) (dual of [8388602, 8388589, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹³, large, F₆₄, 4) (dual of [large, large−13, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OOA(64²⁹, 4194301, F₆₄, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64²⁹, 8388602, F₆₄, 8) (dual of [8388602, 8388573, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(64²⁹, large, F₆₄, 8) (dual of [large, large−29, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (119, 126, large)-net over F₄	[i]	t-Expansion
2	Digital (120, 126, large)-net over F₄	[i]
3	Digital (121, 126, large)-net over F₄	[i]
4	Digital (122, 126, large)-net over F₄	[i]
5	Digital (123, 126, large)-net over F₄	[i]
6	Digital (119, 127, large)-net over F₄	[i]	Net Duplication
7	Digital (120, 128, large)-net over F₄	[i]
8	Digital (121, 129, large)-net over F₄	[i]
9	Digital (122, 130, large)-net over F₄	[i]
10	Digital (123, 131, large)-net over F₄	[i]
11	Digital (124, 132, large)-net over F₄	[i]
12	Digital (125, 133, large)-net over F₄	[i]
13	Digital (126, 134, large)-net over F₄	[i]
14	Digital (127, 135, large)-net over F₄	[i]
15	Digital (128, 136, large)-net over F₄	[i]
16	Digital (118, 125, large)-net over F₄	[i]	m-Reduction
17	Digital (118, 124, large)-net over F₄	[i]
18	Digital (118, 123, large)-net over F₄	[i]
19	Digital (118, 122, large)-net over F₄	[i]
20	Digital (118, 121, large)-net over F₄	[i]